*4.1.3 Stability VAR model test*

The stability test of the VAR model was used to test IRF and VDC. The stability test for VAR estimation can be seen in **Table 4**.

36.79544, and 12.11161 and which are greater than the critical value of 0.05, namely, 29.79707, 15.49471, and 3.841466, respectively. In this regard, H0 is rejected and H1 is accepted. It implies that all variables have influence in the long term or are cointegrated with each other. Therefore, the next step is to carry out analysis with

**Hypothesized no. of CE(s) Trace static Prob Critical value Variable** None \* 80.84738 0.0000 29.79707 FDR At most 1 \* 36.79544 0.0000 15.49471 NPF At most 2 \* 12.11161 0.0005 3.841466 BOPO

Having tested the existence of VECM, the analysis is to estimate on how shortterm and long-term relationships affect each other. The variables of FDR, NPF, and

**Table 6** shows the influence of each variable to other variables, particularly the relationship between FDR with NPF and FDR with BOPO. The short-term estimation results show that the FDR variable is influenced by the NPF variable in lag 1, which has a positive effect of 1.36%. In lag 2, the relationship of the NPF negatively affects FDR for 0.37%. Furthermore, in lag 3, the NPF has a positive effect to FDR with a value of 0.34%. Then, the FDR variable is influenced negatively by the BOPO

**Table 6** shows the influence of BOPO and FDR to NPF. Results show that the NPF variable is influenced by the BOPO in the first lag which has a negative effect of 0.01% and the second lag also shows a negative effect of 0.02%. Then, the NPF variable is influenced by the BOPO in the third lag which has a positive effect that is 0.005%. Then, the NPF variable influenced by the FDR variable negatively affects

Furthermore, **Table 6** shows the relationship between BOPO with FDR and NPF. Empirically, BOPO is influenced positively by the FDR variable in the first and second lags for 0.12 and 0.11%, respectively, but in the third lag, the variables have a negative effect of 0.22%. On the contrary, the BOPO is influenced by the NPF,

and 0.60%, respectively, but in the third lag, it shows a positive effect on the

**Table 7** shows the summary of direction among variables. Results generally indicate that NPF has positive effects toward FDR and BOPO. It implies that NPF that is a proxy variable for financing risk could trigger other risk occurrence,

Based on **Table 8**, VECM estimation analyzes the influence of variables in the long term. The FDR variable is influenced by NPF and BOPO variables. In the first lag, the FDR variable was influenced negatively by 72.58%. However, in contrast to the first lag, the FDR variable was influenced positively by BOPO for 9.02%. The NPF variable is influenced by the BOPO variable and the FDR variable. In the first lag, both variables negatively affect the values of 0.12 and 0.01%. The BOPO variables are influenced by FDR and NPF variables. In the first lag, the BOPO variable is

which has a negative effect on the first lag and third lag, which is 0.95

namely, liquidity and operational risks, in the short run.

BOPO show the significant effect on lag 3 in monthly data.

the VECM estimation.

*Sources: Author's calculation. \*5% level of significance.*

*Risk Analyses on Islamic Banks in Indonesia DOI: http://dx.doi.org/10.5772/intechopen.92245*

**Table 5.** *Cointegration test.*

*4.1.5 VECM estimation*

in the first lag until the third.

the first lag until lag 3.

BOPO, namely, 1%.

**61**

Based on **Table 4**, it can be explained that the model used is stable in lags of 0–3. This can be seen from the range of modules with an average value of less than one. Therefore, the results of the IRF and VDC analyses are valid, so that the cointegration test can be done.

## *4.1.4 Cointegration test*

The fourth stage that must be passed in the VECM estimation is the cointegration test. Cointegration tests are conducted to determine whether there is a long-term relationship on each variable. If there is no cointegration relationship, the VECM estimation cannot be used. This study uses the Johansen cointegration test method available in EViews 7.2 software with a critical value of 0.05. The cointegration test results are shown in **Table 5** as follows.

Based on **Table 5**, at the 5% test level, there are three ranks of cointegration variables. This can be proven from the values of trace statistic, which are 80.84738,


*Sources: Author's calculation.*

*\*5% level of significance.*

#### **Table 3.**

*Lag length criteria.*


**Table 4.** *Test of VAR stability.*


#### **Table 5.**

on the sequential modified LR test statistical criteria. The lag length that was

in lag 3, that is, with the sequential modified LR test statistic 24.77971, PPE

Therefore, the results of the IRF and VDC analyses are valid, so that the

The fourth stage that must be passed in the VECM estimation is the

method available in EViews 7.2 software with a critical value of 0.05. The

cointegration test results are shown in **Table 5** as follows.

cointegration test. Cointegration tests are conducted to determine whether there is a long-term relationship on each variable. If there is no cointegration relationship, the VECM estimation cannot be used. This study uses the Johansen cointegration test

Based on **Table 5**, at the 5% test level, there are three ranks of cointegration variables. This can be proven from the values of trace statistic, which are 80.84738,

**Lag LogL LR FPE AIC** 502.5902 NA 4.943996 10.11180 491.1235 22.01603 4.706602 10.06247 479.1256 22.31603 4.435183 10.00251 465.3591 24.77971\* 4.037246\* 9.907182\*

**Root Modules** 0.165181–0.446285i 0.475873 0.165181 + 0.446285i 0.475873 0.239743–0.404530i 0.470235 0.239743 + 0.404530i 0.470235 0.239164–0.036076i 0.241869 0.239164 + 0.036076i 0.241869

Based on **Table 3**, the optimal lag on all variables from FDR, NPF, and BOPO is

The stability test of the VAR model was used to test IRF and VDC. The stability

Based on **Table 4**, it can be explained that the model used is stable in lags of 0–3. This can be seen from the range of modules with an average value of less than one.

4.037246, and AIC 9.907182. Therefore, the optimal lag has been statistically deter-

included in this study is from 0 to 3.

*4.1.3 Stability VAR model test*

*Banking and Finance*

cointegration test can be done.

*4.1.4 Cointegration test*

*Sources: Author's calculation. \*5% level of significance.*

*Sources: Author's calculation.*

*Test of VAR stability.*

**Table 3.** *Lag length criteria.*

**Table 4.**

**60**

mined and the VAR stability test is carried out.

test for VAR estimation can be seen in **Table 4**.

*Cointegration test.*

36.79544, and 12.11161 and which are greater than the critical value of 0.05, namely, 29.79707, 15.49471, and 3.841466, respectively. In this regard, H0 is rejected and H1 is accepted. It implies that all variables have influence in the long term or are cointegrated with each other. Therefore, the next step is to carry out analysis with the VECM estimation.
